
where \({\rm Exp }\)  denotes the plethystic exponential, \(P_{\mathcal {M}_\sigma (k\gamma )}\)  the monodromic mixed Hodge module on \(\mathcal {M}_\sigma (k\gamma )\)  constructed in [1]} using the orientation data, and \(H_c(M,P)\)  the Hodge polynomial of the cohomology with compact support on \(M\)  with values in \(P\) . In the case of quiver with potentials and King stability conditions, these invariants are integer by [2]}, and we conjecture that this remains true in this more general framework. In particular, we conjecture that as in [2]}:
\(\Omega _\sigma (k\gamma )=H_c(M_\sigma (k\gamma ),\mathcal {H}^1(JH_!P_{\mathcal {M}_\sigma (k\gamma )}))\) 
